That's me. I usually have an ice chest full of ice before I ever leave the house. Deer/hogs get gutted as soon as they're down, next stop is on my hoist to be skinned and put in cooler.I have had it both ways. Sometimes its cold enough it hangs outside overnight.
One thing I can assure you, my deer are quickly gutted and cooled. I am not one of those guys that want to haul it around all day and show it off.
On the odd days that the weather is cold and predicted to be so for a few days, I'll skin and let hang. The meat shrinks as it ages, and the minute fibers will break since it's connected to the bone. That results in tender cuts of muscle (steaks, roasts). For ground meat it makes little difference.
Temperature is everything - regardless of which method you prefer. Cold meat (as in very very cold) is much easier to slice accurately.